The Finster head is a miscellaneous item that can be looted upon his death on the upper level of the Darwin base. The ultimate purpose of its existence is to gain a plot essential item: Secpass B.
By passing an IQ or Cyborg Tech check, one can use the Mindlink with the head to gain entry to the Mindmaze. Successfully completing each of the various challenges presents the victor with Secpass B as an attempt by Finster to aid the Rangers in stopping the menace within Cochise. This ultimately grants access to the 7 suits of Pseudo-Chitin residing in the Sleeper Base, making a raid on the Citadel much more feasible.